If you're a breaststroke swimmer, you might think you know all about frog swimming. But take a closer look and you'll find that there's a lot more going on. For a start, many frog swimmers do more than simply push off with their legs; some row with their paddle-like feet by rotating their ankles to push against the water. But how much of a contribution do leg-pushes and foot-paddles make as a frog moves through its complex aquatic world? Curious to find out more, Christopher Richards decided to film swimming frogs to determine exactly how they move and then built a mathematical frog to dissect out the leg and foot-paddles' contributions to frog propulsion(p. 3181).

Richards explains that he chose to work with African clawed frogs, Xenopus laevis, because they are pure swimmers, spending all of their lives in water. `Their legs are super muscular and they are very powerful animals,' says Richards, adding that handling the slimy creatures as they struggled to get free while he superglued markers to their legs and body was quite challenging. And getting the frogs to swim was even trickier; `they become habituated to the tank and are reluctant to swim,' he explains. The frogs seemed to respond best when he turned on the lights to startle them.

After weeks of patiently waiting for the frogs to swim and analysing their style, Richards set about developing a mathematical model of the frogs'swimming through water so that he could calculate the contributions of their pushing legs and rotating feet to propulsion. He admits that getting the model to work was difficult, as he had to model the behaviour of each joint in the leg and ankle as well as the interaction between the animal's foot-paddles and the water it dragged along. But Richards eventually found a piece of software that could solve the complex equations of motion and was able to begin modelling the animal's behaviour.

Simulating frogs swimming normally, as well as only kicking their legs or only rowing with their feet, Richards discovered that the animals rely far more on their feet rotating than on their leg pushes. The mathematical frogs only reached a top speed of 0.38 m s–1 when powered by leg pushes alone but rocketed to 0.54 m s–1 when powered entirely by foot rowing. Analysing the simulations based on real swimming strokes,Richards realised that the frogs depend on their leg pushes at the beginning of a stroke but that their rotating feet take over later in the stroke,providing the majority of the thrust. Richards also noticed that the frogs decelerated more towards the end of a stroke when kicking with their legs alone because of water resistance caused by their feet sticking out. By rotating their feet at the end of the stroke, the foot-rowing frogs were able to reduce the resistance significantly.

Satisfied that his mathematical frog is working as well as the real thing,Richards is keen to use his model to find out how other frogs propel themselves through water, as well as to understand how the animal's powerful leg muscles operate over multiple joints to generate the frog's hefty swimming kick.

Richards, C. T. (
). The kinematic determinants of anuran swimming performance: an inverse and forward dynamics approach.
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